what do total utilitarians and average utilitarians actually mean when they're talking about the sum or the average of several utility functions?
They don't know. In most cases, they just sort of wave their hands. You can combine utility functions, but "sum" and "average" do not uniquely identify methods for doing so, and no method identified so far has seemed uniquely compelling.
This is for anyone in the LessWrong community who has made at least some effort to read the sequences and follow along, but is still confused on some point, and is perhaps feeling a bit embarrassed. Here, newbies and not-so-newbies are free to ask very basic but still relevant questions with the understanding that the answers are probably somewhere in the sequences. Similarly, LessWrong tends to presume a rather high threshold for understanding science and technology. Relevant questions in those areas are welcome as well. Anyone who chooses to respond should respectfully guide the questioner to a helpful resource, and questioners should be appropriately grateful. Good faith should be presumed on both sides, unless and until it is shown to be absent. If a questioner is not sure whether a question is relevant, ask it, and also ask if it's relevant.